﻿using System;
using System.Collections.Generic;

namespace ProblemsSet
{
    public class Problem_21 : BaseProblem
    {
        public override object GetResult()
        {
            var dict = new Dictionary<long, long>();
            const long max = 10000;
            long res = 0;
            long summ = 0;
            for (var i=2; i < max; i++)
            {
                if (dict.ContainsKey(i))
                {
                    res = dict[i];
                }
                else
                {
                    MathLogic.GetFactors(i, out res);
                    res -= i;
                    dict.Add(i, res);
                }
                long tmp = 0;
                if (dict.ContainsKey(res))
                {
                    tmp = dict[res];
                }
                else
                {
                    MathLogic.GetFactors(res, out tmp);
                    tmp -= res;
                    dict.Add(res, tmp);
                }

                if (tmp != i || i == res) continue;
                summ += i;

            }
            
            return summ;
        }

        public override string Problem
        {
            get
            {
                return @"Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
If d(a) = b and d(b) = a, where a  b, then a and b are an amicable pair and each of a and b are called amicable numbers.

For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.

Evaluate the sum of all the amicable numbers under 10000.";
            }
        }

        
        public override bool IsSolved
        {
            get
            {
                return true;
            }
        }

        public override object Answer
        {
            get
            {
                return 31626;
            }
        }

    }
}
